A novel method for learning characteristic decision trees is applied to the problem of learning the decision mechanism of coin-sorting machines. Decision trees constructed by ID3-like algorithms are unable to detect instances of categories not present in the set of training examples. Instead of being rejected, such instances are assigned to one of the classes actually present in the training set. To solve this problem the algorithm must learn characteristic, rather than discriminative, category descriptions. In addition, the ability to control the degree of generalization is identified as an essential property of such algorithms. A novel method using the information about the statistical distribution of the feature values that can be extracted from the training examples is developed to meet these requirements. The central idea is to augment each leaf of the decision tree with a subtree that imposes further restrictions on the values of each feature in that leaf.